Definitions for tangent scale

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An arc of a circle in which the number of graduations in any arc starting from zero are proportional to the tangent of the angle subtended by such arc. The system is for use with tangent galvanometers. Thus if for 45° a value of 100 is taken and marked on the scale then for the arc 26° 33' + a value of 50 should be marked on the scale because such are the relative values of the tangents. Thus the scale instead of being divided into degrees is divided into arcs of varying length, growing shorter as they are more distant from the zero point, of such length that the first division being subtended by a tangent of length 1, the first and second divisions added or taken together as one arc are subtended by a tangent of length 2, and so on. In the cut a simple method of graphically laying out a tangent scale is shown. In it C is the centre of the arc, and H the radius running to the zero of the instrument. From C a circle is described and on H a vertical line tangent to the arc is erected. Taking any part of the tangent, as the length shown ending at D, it is divided into any number of equal parts. Radii of the circle are now drawn whose prolongations pass through the divisions on the tangent. These radii, where they intersect the arc of the circle, determine equal divisions of the tangent scale, which, as is evident from the construction, are unequal angular divisions of the arc.

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